Which of these numbers is prime? ${27,\ 51,\ 62,\ 81,\ 83}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 27 are 1, 3, 9, and 27. The factors of 51 are 1, 3, 17, and 51. The factors of 62 are 1, 2, 31, and 62. The factors of 81 are 1, 3, 9, 27, and 81. The factors of 83 are 1 and 83. Thus, 83 is a prime number.